I watched a debate between Lawrence Krauss and Hamza Tzortzis about Islam (Here)
At a given point, there was an argument about Infinity and the fact that there's no actual infinity, i.e. in the physical world (this was Tzortzis' claim). Pr. Krauss then drew a circle on a paper with the implicit argument that we can see the number Pi, which requires inifinity for its definition. Although I totally disagree with Tzortzis' opinion, I think Pr. Krauss's argument was incorrect.
To me, what he actually drew on his paper was a bunch of carbone atoms lying on the vertexes of a regular polygon, not a circle. A circle is the limit (in the mathematical sense) as these atoms gets closer and closer.
Ininity is only an mental idea (although a very beautiful idea !) and there's no physical infinity (although Cosmologists are still debating on wether the universe is infinite)

(19-12-2015 12:50 PM)aguelmame Wrote: I watched a debate between Lawrence Krauss and Hamza Tzortzis about Islam (Here)
At a given point, there was an argument about Infinity and the fact that there's no actual infinity, i.e. in the physical world (this was Tzortzis' claim). Pr. Krauss then drew a circle on a paper with the implicit argument that we can see the number Pi, which requires inifinity for its definition. Although I totally disagree with Tzortzis' opinion, I think Pr. Krauss's argument was incorrect.
To me, what he actually drew on his paper was a bunch of carbone atoms lying on the vertexes of a regular polygon, not a circle. A circle is the limit (in the mathematical sense) as these atoms gets closer and closer.
Ininity is only an mental idea (although a very beautiful idea !) and there's no physical infinity (although Cosmologists are still debating on wether the universe is infinite)

I would be happy to hear your opinions about this.

Do you also believe that, because there are negative numbers on a number line, there is negative distance?

How many sides do you think Dr Krauss' polygon had? You do realize that the carbon atoms aren't actually touching each other, right? Are you next going to say it wasn't a circle, since it wasn't a continuous line? You're caught up in logic-chopping.

If Big Bang theory is right, time began at the moment of the "bang" and according to most physicists, our universe would seize to exist at some point. So may be the problem with infinity is just a made-up one?

all of the mathematics used to formula the laws of physics as we know them today necessarily involve infinity at least implicitly. Transcendental numbers, such as pi, are completely unavoidable--the permeability of free space, for example, is defined exactly in terms of pi. However, all these numbers are infinite inasmuch as you need to use a mathematical limit as something goes to infinity. "Limits as something goes to infinity" can be defined in a way such that don't make reference to infinity.

Are physical quantities necessarily finite? Who knows. Gravitational singularities are expected from Einstein's equations, and black holes may be such that example. I'm not sure if these have been observed; don't pay that much attention to astro. In general, yes we expect observable physical quantities to be finite to be observable, but that's just because we haven't observed an infinite observable.

In terms of Krauss's comment, I see it as a mater of semantics more than anything. Are we gonna include mathematical machinery as "real"? That's really the heart of the question, and I don't find hat an interesting question to answer, because by the time you get to answering you really wouldn't have learned one iota about the universe. Mathematics needs infinity (particularly limits thereeof) to make sense including mathematics physicists use; but we generally don't expect observables to be infinite. That's all you're going to come back to, to be honest.

(19-12-2015 01:37 PM)Fireball Wrote: Do you also believe that, because there are negative numbers on a number line, there is negative distance?

How many sides do you think Dr Krauss' polygon had? You do realize that the carbon atoms aren't actually touching each other, right? Are you next going to say it wasn't a circle, since it wasn't a continuous line? You're caught up in logic-chopping.

I don't think I understand you remark. And I don't think you catched mine neither.
Pr Krauss' polygon has a finite number of vertices. And that's the whole point. If you measure the perimeter of a polygon, no matter how large its number of vertices is, you arrive at an approximation of 2*Pi*R. This approximation gets better and better but is never equal to 2*Pi*R in the mathematical sense.
Not to mention other tricky aspects such as how to define the distance between two atoms (distance between their pseudo center of mass, distance between electrons' orbits, ...) and how to actually measure this distance without hitting the wall of Heisenberg incertainty principle.
There's also another difficulty with the Euclidean distance which requires the definition of the square root function, which in turn requires infinity.

all of the mathematics used to formula the laws of physics as we know them today necessarily involve infinity at least implicitly. Transcendental numbers, such as pi, are completely unavoidable--the permeability of free space, for example, is defined exactly in terms of pi. However, all these numbers are infinite inasmuch as you need to use a mathematical limit as something goes to infinity. "Limits as something goes to infinity" can be defined in a way such that don't make reference to infinity.

Are physical quantities necessarily finite? Who knows. Gravitational singularities are expected from Einstein's equations, and black holes may be such that example. I'm not sure if these have been observed; don't pay that much attention to astro. In general, yes we expect observable physical quantities to be finite to be observable, but that's just because we haven't observed an infinite observable.

In terms of Krauss's comment, I see it as a mater of semantics more than anything. Are we gonna include mathematical machinery as "real"? That's really the heart of the question, and I don't find hat an interesting question to answer, because by the time you get to answering you really wouldn't have learned one iota about the universe. Mathematics needs infinity (particularly limits thereeof) to make sense including mathematics physicists use; but we generally don't expect observables to be infinite. That's all you're going to come back to, to be honest.

Dear ZoraPrime,
There are actually some mathematicians, although not many, trying to redo mathematics without the recourse to real numbers (see for instance Norman Wildberger, Youtube channel Here. Actually, he calls people using real numbers "believers" !).
If you read french, you can also have a look at an interesting paper about the necessity of ininity in mathematics Here .

I find it enriching to think about what Pr. Eugene Wigner called "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" and I think we can learn about the universe by asking theses questions (Paul Dirac used to say that if a physical law was not mathematically "elegant", it is likely to be incorrect).

But, Prof Krauss is using a quick, two second doodle to explain something.

Focusing on just one, tiny, fraction of the whole longer debate.... kind of misses things, don't you think?

As for math? Yeah, I haven't really bothered with anything complicated since High school.

Hi Peebothuhul,
I didn't focus on this single point. I watched the whole debate. I'm a big fan of Pr. Krauss.
I just wanted to discuss with other people this rather technical point. My aim was not to weaken in any mean Pr. Krauss' arguments.